TSTP Solution File: SEU291+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU291+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:43:52 EDT 2023
% Result : Theorem 23.17s 3.87s
% Output : Proof 23.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU291+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.35 % Computer : n001.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Wed Aug 23 17:14:24 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.08/1.12 Prover 4: Preprocessing ...
% 3.08/1.12 Prover 1: Preprocessing ...
% 3.28/1.16 Prover 3: Preprocessing ...
% 3.28/1.16 Prover 6: Preprocessing ...
% 3.28/1.16 Prover 5: Preprocessing ...
% 3.28/1.16 Prover 0: Preprocessing ...
% 3.28/1.16 Prover 2: Preprocessing ...
% 6.34/1.62 Prover 5: Proving ...
% 6.79/1.63 Prover 1: Warning: ignoring some quantifiers
% 6.79/1.64 Prover 2: Proving ...
% 6.79/1.65 Prover 3: Warning: ignoring some quantifiers
% 6.96/1.67 Prover 6: Proving ...
% 6.96/1.67 Prover 1: Constructing countermodel ...
% 6.96/1.68 Prover 3: Constructing countermodel ...
% 6.96/1.70 Prover 4: Warning: ignoring some quantifiers
% 7.48/1.75 Prover 4: Constructing countermodel ...
% 7.76/1.80 Prover 0: Proving ...
% 9.17/2.00 Prover 3: gave up
% 9.17/2.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.17/2.07 Prover 7: Preprocessing ...
% 9.17/2.08 Prover 1: gave up
% 9.17/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.17/2.11 Prover 8: Preprocessing ...
% 10.45/2.19 Prover 7: Warning: ignoring some quantifiers
% 10.86/2.20 Prover 7: Constructing countermodel ...
% 10.86/2.26 Prover 8: Warning: ignoring some quantifiers
% 11.34/2.29 Prover 8: Constructing countermodel ...
% 12.44/2.49 Prover 7: gave up
% 13.00/2.50 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 13.00/2.52 Prover 9: Preprocessing ...
% 13.57/2.58 Prover 8: gave up
% 13.57/2.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.57/2.62 Prover 10: Preprocessing ...
% 14.53/2.73 Prover 10: Warning: ignoring some quantifiers
% 14.53/2.73 Prover 10: Constructing countermodel ...
% 14.53/2.74 Prover 9: Warning: ignoring some quantifiers
% 14.53/2.74 Prover 9: Constructing countermodel ...
% 15.44/2.85 Prover 10: gave up
% 15.44/2.85 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.44/2.89 Prover 11: Preprocessing ...
% 17.25/3.07 Prover 11: Warning: ignoring some quantifiers
% 17.25/3.08 Prover 11: Constructing countermodel ...
% 23.17/3.87 Prover 4: Found proof (size 140)
% 23.17/3.87 Prover 4: proved (3209ms)
% 23.17/3.87 Prover 9: stopped
% 23.17/3.87 Prover 11: stopped
% 23.17/3.87 Prover 2: stopped
% 23.17/3.87 Prover 6: stopped
% 23.17/3.87 Prover 5: stopped
% 23.17/3.87 Prover 0: stopped
% 23.17/3.87
% 23.17/3.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.17/3.87
% 23.17/3.88 % SZS output start Proof for theBenchmark
% 23.17/3.88 Assumptions after simplification:
% 23.17/3.88 ---------------------------------
% 23.17/3.88
% 23.17/3.88 (d1_funct_2)
% 23.50/3.92 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.50/3.92 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.50/3.92 $i(v0) | ? [v4: any] : ? [v5: any] : (relation_of2_as_subset(v2, v0, v1) =
% 23.50/3.92 v4 & quasi_total(v2, v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v1 = empty_set) |
% 23.50/3.92 v0 = empty_set | (( ~ (v5 = 0) | v2 = empty_set) & ( ~ (v2 =
% 23.50/3.92 empty_set) | v5 = 0))) & ((v1 = empty_set & ~ (v0 =
% 23.50/3.92 empty_set)) | (( ~ (v5 = 0) | v3 = v0) & ( ~ (v3 = v0) | v5 =
% 23.50/3.92 0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 23.50/3.92 any] : ( ~ (quasi_total(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.50/3.92 $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_dom_as_subset(v0, v1, v2) =
% 23.50/3.92 v5 & relation_of2_as_subset(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | ((
% 23.50/3.92 ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 =
% 23.50/3.92 empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set
% 23.50/3.92 & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 = 0) & ( ~ (v3 = 0) |
% 23.50/3.92 v5 = v0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 23.50/3.92 (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 23.50/3.92 | ? [v3: any] : ? [v4: $i] : (relation_dom_as_subset(v0, v1, v2) = v4 &
% 23.50/3.92 quasi_total(v2, v0, v1) = v3 & $i(v4) & ( ~ (v1 = empty_set) | v0 =
% 23.50/3.92 empty_set | (( ~ (v3 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v3
% 23.50/3.92 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v4 = v0) |
% 23.50/3.92 v3 = 0) & ( ~ (v3 = 0) | v4 = v0)))))
% 23.50/3.92
% 23.50/3.92 (dt_k4_relset_1)
% 23.50/3.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.50/3.92 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.50/3.92 $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (relation_of2(v2, v0,
% 23.50/3.92 v1) = v4 & powerset(v0) = v5 & element(v3, v5) = v6 & $i(v5) & ( ~ (v4 =
% 23.50/3.92 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 23.50/3.92 (relation_of2(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 23.50/3.92 $i] : ? [v4: $i] : (relation_dom_as_subset(v0, v1, v2) = v3 &
% 23.50/3.92 powerset(v0) = v4 & element(v3, v4) = 0 & $i(v4) & $i(v3)))
% 23.50/3.92
% 23.50/3.92 (fc5_relat_1)
% 23.50/3.92 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 23.50/3.92 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 &
% 23.50/3.92 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 23.50/3.92 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 23.50/3.92 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 23.50/3.92 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) &
% 23.50/3.92 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 23.50/3.92 : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 &
% 23.50/3.92 $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 23.50/3.92
% 23.50/3.92 (rc2_relat_1)
% 23.50/3.92 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1
% 23.50/3.92 & $i(v0))
% 23.50/3.92
% 23.50/3.92 (redefinition_k4_relset_1)
% 23.50/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.50/3.93 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.50/3.93 $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_dom(v2) = v5 &
% 23.50/3.93 relation_of2(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3))) & !
% 23.50/3.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1) = 0) | ~
% 23.50/3.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (relation_dom(v2) = v3 &
% 23.50/3.93 relation_dom_as_subset(v0, v1, v2) = v3 & $i(v3)))
% 23.50/3.93
% 23.50/3.93 (redefinition_m2_relset_1)
% 23.50/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 23.50/3.93 (relation_of2(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 23.50/3.93 [v4: int] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & !
% 23.50/3.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 23.50/3.93 (relation_of2_as_subset(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.50/3.93 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & !
% 23.50/3.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1) = 0) | ~
% 23.50/3.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2_as_subset(v2, v0, v1) = 0) &
% 23.50/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0,
% 23.50/3.93 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2(v2, v0, v1)
% 23.50/3.93 = 0)
% 23.50/3.93
% 23.50/3.93 (t16_relset_1)
% 23.50/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 23.50/3.93 | ~ (subset(v0, v1) = 0) | ~ (relation_of2_as_subset(v3, v2, v1) = v4) |
% 23.50/3.93 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 23.50/3.93 relation_of2_as_subset(v3, v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : !
% 23.50/3.93 [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 23.50/3.93 (relation_of2_as_subset(v3, v2, v1) = v4) | ~ (relation_of2_as_subset(v3,
% 23.50/3.93 v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 23.50/3.93 int] : ( ~ (v5 = 0) & subset(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 23.50/3.93 ! [v2: $i] : ! [v3: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 23.50/3.93 (relation_of2_as_subset(v3, v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 23.50/3.93 | ~ $i(v0) | relation_of2_as_subset(v3, v2, v1) = 0)
% 23.50/3.93
% 23.50/3.93 (t3_xboole_1)
% 23.50/3.93 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)
% 23.50/3.93 | ~ $i(v0))
% 23.50/3.93
% 23.50/3.93 (t9_funct_2)
% 23.50/3.93 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 23.50/3.93 [v4: any] : ? [v5: any] : (subset(v1, v2) = 0 & relation_of2_as_subset(v3,
% 23.50/3.93 v0, v2) = v5 & relation_of2_as_subset(v3, v0, v1) = 0 & quasi_total(v3,
% 23.50/3.93 v0, v2) = v4 & quasi_total(v3, v0, v1) = 0 & function(v3) = 0 & $i(v3) &
% 23.50/3.93 $i(v2) & $i(v1) & $i(v0) & ( ~ (v5 = 0) | ~ (v4 = 0)) & ( ~ (v1 =
% 23.50/3.93 empty_set) | v0 = empty_set))
% 23.50/3.93
% 23.50/3.93 (function-axioms)
% 23.50/3.93 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 23.50/3.93 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~
% 23.50/3.93 (relation_of2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.50/3.93 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2)
% 23.50/3.93 = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) & ! [v0:
% 23.50/3.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 23.50/3.94 : ! [v4: $i] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~
% 23.50/3.94 (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 23.50/3.94 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 23.50/3.94 ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0)) & !
% 23.50/3.94 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 23.50/3.94 $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & !
% 23.50/3.94 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.50/3.94 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 23.50/3.94 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 23.50/3.94 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 23.50/3.94 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 23.50/3.94 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i]
% 23.50/3.94 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 23.50/3.94 (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 23.50/3.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 23.50/3.94 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 23.50/3.94 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 23.50/3.94 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: $i] :
% 23.50/3.94 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 23.50/3.94 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 23.50/3.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 23.50/3.94 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 23.50/3.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 23.50/3.94 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 23.50/3.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 23.50/3.94 (empty(v2) = v0))
% 23.50/3.94
% 23.50/3.94 Further assumptions not needed in the proof:
% 23.50/3.94 --------------------------------------------
% 23.50/3.94 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc1_relset_1, cc2_funct_1,
% 23.50/3.94 dt_k1_relat_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_m1_relset_1,
% 23.50/3.94 dt_m1_subset_1, dt_m2_relset_1, existence_m1_relset_1, existence_m1_subset_1,
% 23.50/3.94 existence_m2_relset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1,
% 23.50/3.94 fc4_subset_1, fc7_relat_1, rc1_funct_1, rc1_funct_2, rc1_partfun1, rc1_relat_1,
% 23.50/3.94 rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_partfun1, rc2_subset_1,
% 23.50/3.94 rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1, reflexivity_r1_tarski,
% 23.50/3.94 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 23.50/3.94 t8_boole
% 23.50/3.94
% 23.50/3.94 Those formulas are unsatisfiable:
% 23.50/3.94 ---------------------------------
% 23.50/3.94
% 23.50/3.94 Begin of proof
% 23.50/3.94 |
% 23.50/3.94 | ALPHA: (d1_funct_2) implies:
% 23.50/3.94 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 23.50/3.94 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 23.50/3.94 | $i(v0) | ? [v3: any] : ? [v4: $i] : (relation_dom_as_subset(v0, v1,
% 23.50/3.94 | v2) = v4 & quasi_total(v2, v0, v1) = v3 & $i(v4) & ( ~ (v1 =
% 23.50/3.94 | empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 = empty_set) &
% 23.50/3.94 | ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set & ~ (v0 =
% 23.50/3.94 | empty_set)) | (( ~ (v4 = v0) | v3 = 0) & ( ~ (v3 = 0) | v4 =
% 23.50/3.94 | v0)))))
% 23.50/3.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 23.50/3.94 | (quasi_total(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 23.50/3.94 | ? [v4: any] : ? [v5: $i] : (relation_dom_as_subset(v0, v1, v2) = v5
% 23.50/3.94 | & relation_of2_as_subset(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) |
% 23.50/3.94 | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 =
% 23.50/3.94 | empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 =
% 23.50/3.94 | empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 = 0)
% 23.50/3.94 | & ( ~ (v3 = 0) | v5 = v0)))))))
% 23.50/3.94 |
% 23.50/3.94 | ALPHA: (dt_k4_relset_1) implies:
% 23.50/3.94 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1)
% 23.50/3.94 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 23.50/3.94 | $i] : (relation_dom_as_subset(v0, v1, v2) = v3 & powerset(v0) = v4
% 23.50/3.94 | & element(v3, v4) = 0 & $i(v4) & $i(v3)))
% 23.50/3.94 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.50/3.94 | (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 23.50/3.94 | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 23.50/3.94 | (relation_of2(v2, v0, v1) = v4 & powerset(v0) = v5 & element(v3, v5)
% 23.50/3.94 | = v6 & $i(v5) & ( ~ (v4 = 0) | v6 = 0)))
% 23.50/3.94 |
% 23.50/3.94 | ALPHA: (fc5_relat_1) implies:
% 23.50/3.94 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0)
% 23.50/3.94 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3
% 23.50/3.94 | & relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~
% 23.50/3.94 | (v2 = 0))))
% 23.50/3.94 |
% 23.50/3.94 | ALPHA: (redefinition_k4_relset_1) implies:
% 23.50/3.94 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1)
% 23.50/3.94 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 23.50/3.94 | (relation_dom(v2) = v3 & relation_dom_as_subset(v0, v1, v2) = v3 &
% 23.50/3.94 | $i(v3)))
% 23.50/3.95 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.50/3.95 | (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 23.50/3.95 | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_dom(v2) = v5 &
% 23.50/3.95 | relation_of2(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3)))
% 23.50/3.95 |
% 23.50/3.95 | ALPHA: (redefinition_m2_relset_1) implies:
% 23.50/3.95 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 23.50/3.95 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 23.50/3.95 | $i(v0) | relation_of2(v2, v0, v1) = 0)
% 23.50/3.95 |
% 23.50/3.95 | ALPHA: (t16_relset_1) implies:
% 23.50/3.95 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (subset(v0,
% 23.50/3.95 | v1) = 0) | ~ (relation_of2_as_subset(v3, v2, v0) = 0) | ~
% 23.50/3.95 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 23.50/3.95 | relation_of2_as_subset(v3, v2, v1) = 0)
% 23.50/3.95 |
% 23.50/3.95 | ALPHA: (t3_xboole_1) implies:
% 23.50/3.95 | (10) ! [v0: $i] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0) | ~
% 23.50/3.95 | $i(v0))
% 23.50/3.95 |
% 23.50/3.95 | ALPHA: (t9_funct_2) implies:
% 23.50/3.95 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 23.50/3.95 | ? [v5: any] : (subset(v1, v2) = 0 & relation_of2_as_subset(v3, v0,
% 23.50/3.95 | v2) = v5 & relation_of2_as_subset(v3, v0, v1) = 0 &
% 23.50/3.95 | quasi_total(v3, v0, v2) = v4 & quasi_total(v3, v0, v1) = 0 &
% 23.50/3.95 | function(v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v5 = 0)
% 23.50/3.95 | | ~ (v4 = 0)) & ( ~ (v1 = empty_set) | v0 = empty_set))
% 23.50/3.95 |
% 23.50/3.95 | ALPHA: (function-axioms) implies:
% 23.50/3.95 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 23.50/3.95 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 23.50/3.95 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.50/3.95 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 23.50/3.95 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 23.50/3.95 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) =
% 23.50/3.95 | v1) | ~ (quasi_total(v4, v3, v2) = v0))
% 23.50/3.95 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 23.50/3.95 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 23.50/3.95 | (relation_of2_as_subset(v4, v3, v2) = v1) | ~
% 23.50/3.95 | (relation_of2_as_subset(v4, v3, v2) = v0))
% 23.50/3.95 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 23.50/3.95 | (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~
% 23.50/3.95 | (relation_dom_as_subset(v4, v3, v2) = v0))
% 23.50/3.95 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 23.50/3.95 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2)
% 23.50/3.95 | = v1) | ~ (relation_of2(v4, v3, v2) = v0))
% 23.50/3.95 |
% 23.72/3.95 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_47_0, all_47_1
% 23.72/3.95 | gives:
% 23.72/3.95 | (18) ~ (all_47_0 = 0) & relation(all_47_1) = 0 & empty(all_47_1) =
% 23.72/3.95 | all_47_0 & $i(all_47_1)
% 23.72/3.95 |
% 23.72/3.95 | ALPHA: (18) implies:
% 23.72/3.95 | (19) ~ (all_47_0 = 0)
% 23.72/3.95 | (20) $i(all_47_1)
% 23.72/3.95 | (21) empty(all_47_1) = all_47_0
% 23.72/3.95 | (22) relation(all_47_1) = 0
% 23.72/3.95 |
% 23.72/3.95 | DELTA: instantiating (11) with fresh symbols all_56_0, all_56_1, all_56_2,
% 23.72/3.95 | all_56_3, all_56_4, all_56_5 gives:
% 23.72/3.95 | (23) subset(all_56_4, all_56_3) = 0 & relation_of2_as_subset(all_56_2,
% 23.72/3.95 | all_56_5, all_56_3) = all_56_0 & relation_of2_as_subset(all_56_2,
% 23.72/3.95 | all_56_5, all_56_4) = 0 & quasi_total(all_56_2, all_56_5, all_56_3)
% 23.72/3.95 | = all_56_1 & quasi_total(all_56_2, all_56_5, all_56_4) = 0 &
% 23.72/3.95 | function(all_56_2) = 0 & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) &
% 23.72/3.95 | $i(all_56_5) & ( ~ (all_56_0 = 0) | ~ (all_56_1 = 0)) & ( ~ (all_56_4
% 23.72/3.95 | = empty_set) | all_56_5 = empty_set)
% 23.72/3.95 |
% 23.72/3.95 | ALPHA: (23) implies:
% 23.72/3.95 | (24) $i(all_56_5)
% 23.72/3.95 | (25) $i(all_56_4)
% 23.72/3.96 | (26) $i(all_56_3)
% 23.72/3.96 | (27) $i(all_56_2)
% 23.72/3.96 | (28) quasi_total(all_56_2, all_56_5, all_56_4) = 0
% 23.72/3.96 | (29) quasi_total(all_56_2, all_56_5, all_56_3) = all_56_1
% 23.72/3.96 | (30) relation_of2_as_subset(all_56_2, all_56_5, all_56_4) = 0
% 23.72/3.96 | (31) relation_of2_as_subset(all_56_2, all_56_5, all_56_3) = all_56_0
% 23.72/3.96 | (32) subset(all_56_4, all_56_3) = 0
% 23.72/3.96 | (33) ~ (all_56_4 = empty_set) | all_56_5 = empty_set
% 23.72/3.96 | (34) ~ (all_56_0 = 0) | ~ (all_56_1 = 0)
% 23.72/3.96 |
% 23.72/3.96 | GROUND_INST: instantiating (5) with all_47_1, all_47_0, simplifying with (20),
% 23.72/3.96 | (21) gives:
% 23.72/3.96 | (35) all_47_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 23.72/3.96 | (relation_dom(all_47_1) = v1 & relation(all_47_1) = v0 & empty(v1) =
% 23.72/3.96 | v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.72/3.96 |
% 23.72/3.96 | GROUND_INST: instantiating (2) with all_56_5, all_56_4, all_56_2, 0,
% 23.72/3.96 | simplifying with (24), (25), (27), (28) gives:
% 23.72/3.96 | (36) ? [v0: any] : ? [v1: $i] : (relation_dom_as_subset(all_56_5,
% 23.72/3.96 | all_56_4, all_56_2) = v1 & relation_of2_as_subset(all_56_2,
% 23.72/3.96 | all_56_5, all_56_4) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (all_56_4
% 23.72/3.96 | = empty_set) | all_56_2 = empty_set | all_56_5 = empty_set)
% 23.72/3.96 | & (v1 = all_56_5 | (all_56_4 = empty_set & ~ (all_56_5 =
% 23.72/3.96 | empty_set))))))
% 23.72/3.96 |
% 23.72/3.96 | GROUND_INST: instantiating (2) with all_56_5, all_56_3, all_56_2, all_56_1,
% 23.72/3.96 | simplifying with (24), (26), (27), (29) gives:
% 23.72/3.96 | (37) ? [v0: any] : ? [v1: $i] : (relation_dom_as_subset(all_56_5,
% 23.72/3.96 | all_56_3, all_56_2) = v1 & relation_of2_as_subset(all_56_2,
% 23.72/3.96 | all_56_5, all_56_3) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (all_56_3
% 23.72/3.96 | = empty_set) | all_56_5 = empty_set | (( ~ (all_56_1 = 0) |
% 23.72/3.96 | all_56_2 = empty_set) & ( ~ (all_56_2 = empty_set) |
% 23.72/3.96 | all_56_1 = 0))) & ((all_56_3 = empty_set & ~ (all_56_5 =
% 23.72/3.96 | empty_set)) | (( ~ (v1 = all_56_5) | all_56_1 = 0) & ( ~
% 23.72/3.96 | (all_56_1 = 0) | v1 = all_56_5))))))
% 23.72/3.96 |
% 23.72/3.96 | GROUND_INST: instantiating (8) with all_56_5, all_56_4, all_56_2, simplifying
% 23.72/3.96 | with (24), (25), (27), (30) gives:
% 23.72/3.96 | (38) relation_of2(all_56_2, all_56_5, all_56_4) = 0
% 23.72/3.96 |
% 23.72/3.96 | GROUND_INST: instantiating (1) with all_56_5, all_56_4, all_56_2, simplifying
% 23.72/3.96 | with (24), (25), (27), (30) gives:
% 23.72/3.96 | (39) ? [v0: any] : ? [v1: $i] : (relation_dom_as_subset(all_56_5,
% 23.72/3.96 | all_56_4, all_56_2) = v1 & quasi_total(all_56_2, all_56_5,
% 23.72/3.96 | all_56_4) = v0 & $i(v1) & ( ~ (all_56_4 = empty_set) | all_56_5 =
% 23.72/3.96 | empty_set | (( ~ (v0 = 0) | all_56_2 = empty_set) & ( ~ (all_56_2
% 23.72/3.96 | = empty_set) | v0 = 0))) & ((all_56_4 = empty_set & ~
% 23.72/3.96 | (all_56_5 = empty_set)) | (( ~ (v1 = all_56_5) | v0 = 0) & ( ~
% 23.72/3.96 | (v0 = 0) | v1 = all_56_5))))
% 23.72/3.96 |
% 23.72/3.96 | GROUND_INST: instantiating (9) with all_56_4, all_56_3, all_56_5, all_56_2,
% 23.72/3.96 | simplifying with (24), (25), (26), (27), (30), (32) gives:
% 23.72/3.96 | (40) relation_of2_as_subset(all_56_2, all_56_5, all_56_3) = 0
% 23.72/3.96 |
% 23.72/3.96 | DELTA: instantiating (36) with fresh symbols all_132_0, all_132_1 gives:
% 23.72/3.96 | (41) relation_dom_as_subset(all_56_5, all_56_4, all_56_2) = all_132_0 &
% 23.72/3.96 | relation_of2_as_subset(all_56_2, all_56_5, all_56_4) = all_132_1 &
% 23.72/3.96 | $i(all_132_0) & ( ~ (all_132_1 = 0) | (( ~ (all_56_4 = empty_set) |
% 23.72/3.96 | all_56_2 = empty_set | all_56_5 = empty_set) & (all_132_0 =
% 23.72/3.96 | all_56_5 | (all_56_4 = empty_set & ~ (all_56_5 = empty_set)))))
% 23.72/3.96 |
% 23.72/3.96 | ALPHA: (41) implies:
% 23.72/3.96 | (42) relation_of2_as_subset(all_56_2, all_56_5, all_56_4) = all_132_1
% 23.72/3.96 | (43) relation_dom_as_subset(all_56_5, all_56_4, all_56_2) = all_132_0
% 23.72/3.97 | (44) ~ (all_132_1 = 0) | (( ~ (all_56_4 = empty_set) | all_56_2 =
% 23.72/3.97 | empty_set | all_56_5 = empty_set) & (all_132_0 = all_56_5 |
% 23.72/3.97 | (all_56_4 = empty_set & ~ (all_56_5 = empty_set))))
% 23.72/3.97 |
% 23.72/3.97 | DELTA: instantiating (39) with fresh symbols all_134_0, all_134_1 gives:
% 23.72/3.97 | (45) relation_dom_as_subset(all_56_5, all_56_4, all_56_2) = all_134_0 &
% 23.72/3.97 | quasi_total(all_56_2, all_56_5, all_56_4) = all_134_1 & $i(all_134_0)
% 23.72/3.97 | & ( ~ (all_56_4 = empty_set) | all_56_5 = empty_set | (( ~ (all_134_1
% 23.72/3.97 | = 0) | all_56_2 = empty_set) & ( ~ (all_56_2 = empty_set) |
% 23.72/3.97 | all_134_1 = 0))) & ((all_56_4 = empty_set & ~ (all_56_5 =
% 23.72/3.97 | empty_set)) | (( ~ (all_134_0 = all_56_5) | all_134_1 = 0) & ( ~
% 23.72/3.97 | (all_134_1 = 0) | all_134_0 = all_56_5)))
% 23.72/3.97 |
% 23.72/3.97 | ALPHA: (45) implies:
% 23.72/3.97 | (46) quasi_total(all_56_2, all_56_5, all_56_4) = all_134_1
% 23.72/3.97 | (47) relation_dom_as_subset(all_56_5, all_56_4, all_56_2) = all_134_0
% 23.72/3.97 | (48) (all_56_4 = empty_set & ~ (all_56_5 = empty_set)) | (( ~ (all_134_0 =
% 23.72/3.97 | all_56_5) | all_134_1 = 0) & ( ~ (all_134_1 = 0) | all_134_0 =
% 23.72/3.97 | all_56_5))
% 23.72/3.97 |
% 23.72/3.97 | DELTA: instantiating (37) with fresh symbols all_136_0, all_136_1 gives:
% 23.72/3.97 | (49) relation_dom_as_subset(all_56_5, all_56_3, all_56_2) = all_136_0 &
% 23.72/3.97 | relation_of2_as_subset(all_56_2, all_56_5, all_56_3) = all_136_1 &
% 23.72/3.97 | $i(all_136_0) & ( ~ (all_136_1 = 0) | (( ~ (all_56_3 = empty_set) |
% 23.72/3.97 | all_56_5 = empty_set | (( ~ (all_56_1 = 0) | all_56_2 =
% 23.72/3.97 | empty_set) & ( ~ (all_56_2 = empty_set) | all_56_1 = 0))) &
% 23.72/3.97 | ((all_56_3 = empty_set & ~ (all_56_5 = empty_set)) | (( ~
% 23.72/3.97 | (all_136_0 = all_56_5) | all_56_1 = 0) & ( ~ (all_56_1 = 0)
% 23.72/3.97 | | all_136_0 = all_56_5)))))
% 23.72/3.97 |
% 23.72/3.97 | ALPHA: (49) implies:
% 23.72/3.97 | (50) relation_of2_as_subset(all_56_2, all_56_5, all_56_3) = all_136_1
% 23.72/3.97 | (51) relation_dom_as_subset(all_56_5, all_56_3, all_56_2) = all_136_0
% 23.72/3.97 | (52) ~ (all_136_1 = 0) | (( ~ (all_56_3 = empty_set) | all_56_5 =
% 23.72/3.97 | empty_set | (( ~ (all_56_1 = 0) | all_56_2 = empty_set) & ( ~
% 23.72/3.97 | (all_56_2 = empty_set) | all_56_1 = 0))) & ((all_56_3 =
% 23.72/3.97 | empty_set & ~ (all_56_5 = empty_set)) | (( ~ (all_136_0 =
% 23.72/3.97 | all_56_5) | all_56_1 = 0) & ( ~ (all_56_1 = 0) | all_136_0 =
% 23.72/3.97 | all_56_5))))
% 23.72/3.97 |
% 23.72/3.97 | BETA: splitting (35) gives:
% 23.72/3.97 |
% 23.72/3.97 | Case 1:
% 23.72/3.97 | |
% 23.72/3.97 | | (53) all_47_0 = 0
% 23.72/3.97 | |
% 23.72/3.97 | | REDUCE: (19), (53) imply:
% 23.72/3.97 | | (54) $false
% 23.72/3.97 | |
% 23.72/3.97 | | CLOSE: (54) is inconsistent.
% 23.72/3.97 | |
% 23.72/3.97 | Case 2:
% 23.72/3.97 | |
% 23.72/3.97 | | (55) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_47_1)
% 23.72/3.97 | | = v1 & relation(all_47_1) = v0 & empty(v1) = v2 & $i(v1) & ( ~ (v2
% 23.72/3.97 | | = 0) | ~ (v0 = 0)))
% 23.72/3.97 | |
% 23.72/3.97 | | DELTA: instantiating (55) with fresh symbols all_142_0, all_142_1, all_142_2
% 23.72/3.97 | | gives:
% 23.72/3.97 | | (56) relation_dom(all_47_1) = all_142_1 & relation(all_47_1) = all_142_2
% 23.72/3.97 | | & empty(all_142_1) = all_142_0 & $i(all_142_1) & ( ~ (all_142_0 = 0)
% 23.72/3.97 | | | ~ (all_142_2 = 0))
% 23.72/3.97 | |
% 23.72/3.97 | | ALPHA: (56) implies:
% 23.72/3.97 | | (57) relation(all_47_1) = all_142_2
% 23.72/3.97 | | (58) ~ (all_142_0 = 0) | ~ (all_142_2 = 0)
% 23.72/3.97 | |
% 23.72/3.97 | | BETA: splitting (34) gives:
% 23.72/3.97 | |
% 23.72/3.97 | | Case 1:
% 23.72/3.97 | | |
% 23.72/3.97 | | | (59) ~ (all_56_0 = 0)
% 23.72/3.97 | | |
% 23.72/3.97 | | | GROUND_INST: instantiating (15) with all_56_0, all_136_1, all_56_3,
% 23.72/3.97 | | | all_56_5, all_56_2, simplifying with (31), (50) gives:
% 23.72/3.97 | | | (60) all_136_1 = all_56_0
% 23.72/3.97 | | |
% 23.72/3.97 | | | GROUND_INST: instantiating (15) with 0, all_136_1, all_56_3, all_56_5,
% 23.72/3.97 | | | all_56_2, simplifying with (40), (50) gives:
% 23.72/3.97 | | | (61) all_136_1 = 0
% 23.72/3.97 | | |
% 23.72/3.97 | | | COMBINE_EQS: (60), (61) imply:
% 23.72/3.97 | | | (62) all_56_0 = 0
% 23.72/3.97 | | |
% 23.72/3.97 | | | SIMP: (62) implies:
% 23.72/3.97 | | | (63) all_56_0 = 0
% 23.72/3.97 | | |
% 23.72/3.97 | | | REDUCE: (59), (63) imply:
% 23.72/3.97 | | | (64) $false
% 23.72/3.97 | | |
% 23.72/3.97 | | | CLOSE: (64) is inconsistent.
% 23.72/3.97 | | |
% 23.72/3.97 | | Case 2:
% 23.72/3.97 | | |
% 23.72/3.97 | | | (65) ~ (all_56_1 = 0)
% 23.72/3.97 | | |
% 23.72/3.97 | | | GROUND_INST: instantiating (12) with 0, all_142_2, all_47_1, simplifying
% 23.72/3.97 | | | with (22), (57) gives:
% 23.72/3.97 | | | (66) all_142_2 = 0
% 23.72/3.97 | | |
% 23.72/3.97 | | | GROUND_INST: instantiating (14) with 0, all_134_1, all_56_4, all_56_5,
% 23.72/3.97 | | | all_56_2, simplifying with (28), (46) gives:
% 23.72/3.97 | | | (67) all_134_1 = 0
% 23.72/3.97 | | |
% 23.72/3.97 | | | GROUND_INST: instantiating (15) with 0, all_132_1, all_56_4, all_56_5,
% 23.72/3.97 | | | all_56_2, simplifying with (30), (42) gives:
% 23.72/3.97 | | | (68) all_132_1 = 0
% 23.72/3.97 | | |
% 23.72/3.98 | | | GROUND_INST: instantiating (15) with 0, all_136_1, all_56_3, all_56_5,
% 23.72/3.98 | | | all_56_2, simplifying with (40), (50) gives:
% 23.72/3.98 | | | (69) all_136_1 = 0
% 23.72/3.98 | | |
% 23.72/3.98 | | | GROUND_INST: instantiating (16) with all_132_0, all_134_0, all_56_2,
% 23.72/3.98 | | | all_56_4, all_56_5, simplifying with (43), (47) gives:
% 23.72/3.98 | | | (70) all_134_0 = all_132_0
% 23.72/3.98 | | |
% 23.72/3.98 | | | BETA: splitting (58) gives:
% 23.72/3.98 | | |
% 23.72/3.98 | | | Case 1:
% 23.72/3.98 | | | |
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (8) with all_56_5, all_56_3, all_56_2,
% 23.72/3.98 | | | | simplifying with (24), (26), (27), (40) gives:
% 23.72/3.98 | | | | (71) relation_of2(all_56_2, all_56_5, all_56_3) = 0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (7) with all_56_5, all_56_4, all_56_2,
% 23.72/3.98 | | | | all_132_0, simplifying with (24), (25), (27), (43) gives:
% 23.72/3.98 | | | | (72) ? [v0: any] : ? [v1: $i] : (relation_dom(all_56_2) = v1 &
% 23.72/3.98 | | | | relation_of2(all_56_2, all_56_5, all_56_4) = v0 & $i(v1) & ( ~
% 23.72/3.98 | | | | (v0 = 0) | v1 = all_132_0))
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (4) with all_56_5, all_56_3, all_56_2,
% 23.72/3.98 | | | | all_136_0, simplifying with (24), (26), (27), (51) gives:
% 23.72/3.98 | | | | (73) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 23.72/3.98 | | | | (relation_of2(all_56_2, all_56_5, all_56_3) = v0 &
% 23.72/3.98 | | | | powerset(all_56_5) = v1 & element(all_136_0, v1) = v2 & $i(v1)
% 23.72/3.98 | | | | & ( ~ (v0 = 0) | v2 = 0))
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (7) with all_56_5, all_56_3, all_56_2,
% 23.72/3.98 | | | | all_136_0, simplifying with (24), (26), (27), (51) gives:
% 23.72/3.98 | | | | (74) ? [v0: any] : ? [v1: $i] : (relation_dom(all_56_2) = v1 &
% 23.72/3.98 | | | | relation_of2(all_56_2, all_56_5, all_56_3) = v0 & $i(v1) & ( ~
% 23.72/3.98 | | | | (v0 = 0) | v1 = all_136_0))
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (3) with all_56_5, all_56_4, all_56_2,
% 23.72/3.98 | | | | simplifying with (24), (25), (27), (38) gives:
% 23.72/3.98 | | | | (75) ? [v0: $i] : ? [v1: $i] : (relation_dom_as_subset(all_56_5,
% 23.72/3.98 | | | | all_56_4, all_56_2) = v0 & powerset(all_56_5) = v1 &
% 23.72/3.98 | | | | element(v0, v1) = 0 & $i(v1) & $i(v0))
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (6) with all_56_5, all_56_4, all_56_2,
% 23.72/3.98 | | | | simplifying with (24), (25), (27), (38) gives:
% 23.72/3.98 | | | | (76) ? [v0: $i] : (relation_dom(all_56_2) = v0 &
% 23.72/3.98 | | | | relation_dom_as_subset(all_56_5, all_56_4, all_56_2) = v0 &
% 23.72/3.98 | | | | $i(v0))
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | DELTA: instantiating (76) with fresh symbol all_198_0 gives:
% 23.72/3.98 | | | | (77) relation_dom(all_56_2) = all_198_0 &
% 23.72/3.98 | | | | relation_dom_as_subset(all_56_5, all_56_4, all_56_2) = all_198_0
% 23.72/3.98 | | | | & $i(all_198_0)
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | ALPHA: (77) implies:
% 23.72/3.98 | | | | (78) relation_dom_as_subset(all_56_5, all_56_4, all_56_2) = all_198_0
% 23.72/3.98 | | | | (79) relation_dom(all_56_2) = all_198_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | DELTA: instantiating (75) with fresh symbols all_218_0, all_218_1 gives:
% 23.72/3.98 | | | | (80) relation_dom_as_subset(all_56_5, all_56_4, all_56_2) = all_218_1
% 23.72/3.98 | | | | & powerset(all_56_5) = all_218_0 & element(all_218_1, all_218_0)
% 23.72/3.98 | | | | = 0 & $i(all_218_0) & $i(all_218_1)
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | ALPHA: (80) implies:
% 23.72/3.98 | | | | (81) relation_dom_as_subset(all_56_5, all_56_4, all_56_2) = all_218_1
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | DELTA: instantiating (74) with fresh symbols all_220_0, all_220_1 gives:
% 23.72/3.98 | | | | (82) relation_dom(all_56_2) = all_220_0 & relation_of2(all_56_2,
% 23.72/3.98 | | | | all_56_5, all_56_3) = all_220_1 & $i(all_220_0) & ( ~
% 23.72/3.98 | | | | (all_220_1 = 0) | all_220_0 = all_136_0)
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | ALPHA: (82) implies:
% 23.72/3.98 | | | | (83) relation_of2(all_56_2, all_56_5, all_56_3) = all_220_1
% 23.72/3.98 | | | | (84) relation_dom(all_56_2) = all_220_0
% 23.72/3.98 | | | | (85) ~ (all_220_1 = 0) | all_220_0 = all_136_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | DELTA: instantiating (72) with fresh symbols all_222_0, all_222_1 gives:
% 23.72/3.98 | | | | (86) relation_dom(all_56_2) = all_222_0 & relation_of2(all_56_2,
% 23.72/3.98 | | | | all_56_5, all_56_4) = all_222_1 & $i(all_222_0) & ( ~
% 23.72/3.98 | | | | (all_222_1 = 0) | all_222_0 = all_132_0)
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | ALPHA: (86) implies:
% 23.72/3.98 | | | | (87) relation_dom(all_56_2) = all_222_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | DELTA: instantiating (73) with fresh symbols all_252_0, all_252_1,
% 23.72/3.98 | | | | all_252_2 gives:
% 23.72/3.98 | | | | (88) relation_of2(all_56_2, all_56_5, all_56_3) = all_252_2 &
% 23.72/3.98 | | | | powerset(all_56_5) = all_252_1 & element(all_136_0, all_252_1) =
% 23.72/3.98 | | | | all_252_0 & $i(all_252_1) & ( ~ (all_252_2 = 0) | all_252_0 = 0)
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | ALPHA: (88) implies:
% 23.72/3.98 | | | | (89) relation_of2(all_56_2, all_56_5, all_56_3) = all_252_2
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (16) with all_132_0, all_218_1, all_56_2,
% 23.72/3.98 | | | | all_56_4, all_56_5, simplifying with (43), (81) gives:
% 23.72/3.98 | | | | (90) all_218_1 = all_132_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (16) with all_198_0, all_218_1, all_56_2,
% 23.72/3.98 | | | | all_56_4, all_56_5, simplifying with (78), (81) gives:
% 23.72/3.98 | | | | (91) all_218_1 = all_198_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (17) with all_220_1, all_252_2, all_56_3,
% 23.72/3.98 | | | | all_56_5, all_56_2, simplifying with (83), (89) gives:
% 23.72/3.98 | | | | (92) all_252_2 = all_220_1
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (17) with 0, all_252_2, all_56_3, all_56_5,
% 23.72/3.98 | | | | all_56_2, simplifying with (71), (89) gives:
% 23.72/3.98 | | | | (93) all_252_2 = 0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (13) with all_220_0, all_222_0, all_56_2,
% 23.72/3.98 | | | | simplifying with (84), (87) gives:
% 23.72/3.98 | | | | (94) all_222_0 = all_220_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | GROUND_INST: instantiating (13) with all_198_0, all_222_0, all_56_2,
% 23.72/3.98 | | | | simplifying with (79), (87) gives:
% 23.72/3.98 | | | | (95) all_222_0 = all_198_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | COMBINE_EQS: (92), (93) imply:
% 23.72/3.98 | | | | (96) all_220_1 = 0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | SIMP: (96) implies:
% 23.72/3.98 | | | | (97) all_220_1 = 0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | COMBINE_EQS: (94), (95) imply:
% 23.72/3.98 | | | | (98) all_220_0 = all_198_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | SIMP: (98) implies:
% 23.72/3.98 | | | | (99) all_220_0 = all_198_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | COMBINE_EQS: (90), (91) imply:
% 23.72/3.98 | | | | (100) all_198_0 = all_132_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | COMBINE_EQS: (99), (100) imply:
% 23.72/3.98 | | | | (101) all_220_0 = all_132_0
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | BETA: splitting (85) gives:
% 23.72/3.98 | | | |
% 23.72/3.98 | | | | Case 1:
% 23.72/3.98 | | | | |
% 23.72/3.98 | | | | | (102) ~ (all_220_1 = 0)
% 23.72/3.98 | | | | |
% 23.72/3.98 | | | | | REDUCE: (97), (102) imply:
% 23.72/3.98 | | | | | (103) $false
% 23.72/3.98 | | | | |
% 23.72/3.98 | | | | | CLOSE: (103) is inconsistent.
% 23.72/3.98 | | | | |
% 23.72/3.98 | | | | Case 2:
% 23.72/3.98 | | | | |
% 23.72/3.98 | | | | | (104) all_220_0 = all_136_0
% 23.72/3.98 | | | | |
% 23.72/3.99 | | | | | COMBINE_EQS: (101), (104) imply:
% 23.72/3.99 | | | | | (105) all_136_0 = all_132_0
% 23.72/3.99 | | | | |
% 23.72/3.99 | | | | | BETA: splitting (33) gives:
% 23.72/3.99 | | | | |
% 23.72/3.99 | | | | | Case 1:
% 23.72/3.99 | | | | | |
% 23.72/3.99 | | | | | | (106) ~ (all_56_4 = empty_set)
% 23.72/3.99 | | | | | |
% 23.72/3.99 | | | | | | BETA: splitting (44) gives:
% 23.72/3.99 | | | | | |
% 23.72/3.99 | | | | | | Case 1:
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | (107) ~ (all_132_1 = 0)
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | REDUCE: (68), (107) imply:
% 23.72/3.99 | | | | | | | (108) $false
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | CLOSE: (108) is inconsistent.
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | Case 2:
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | (109) ( ~ (all_56_4 = empty_set) | all_56_2 = empty_set |
% 23.72/3.99 | | | | | | | all_56_5 = empty_set) & (all_132_0 = all_56_5 |
% 23.72/3.99 | | | | | | | (all_56_4 = empty_set & ~ (all_56_5 = empty_set)))
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | ALPHA: (109) implies:
% 23.72/3.99 | | | | | | | (110) all_132_0 = all_56_5 | (all_56_4 = empty_set & ~
% 23.72/3.99 | | | | | | | (all_56_5 = empty_set))
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | BETA: splitting (110) gives:
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | Case 1:
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | (111) all_132_0 = all_56_5
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | COMBINE_EQS: (105), (111) imply:
% 23.72/3.99 | | | | | | | | (112) all_136_0 = all_56_5
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | BETA: splitting (52) gives:
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | Case 1:
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | (113) ~ (all_136_1 = 0)
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | REDUCE: (69), (113) imply:
% 23.72/3.99 | | | | | | | | | (114) $false
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | CLOSE: (114) is inconsistent.
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | Case 2:
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | (115) ( ~ (all_56_3 = empty_set) | all_56_5 = empty_set |
% 23.72/3.99 | | | | | | | | | (( ~ (all_56_1 = 0) | all_56_2 = empty_set) & ( ~
% 23.72/3.99 | | | | | | | | | (all_56_2 = empty_set) | all_56_1 = 0))) &
% 23.72/3.99 | | | | | | | | | ((all_56_3 = empty_set & ~ (all_56_5 = empty_set)) |
% 23.72/3.99 | | | | | | | | | (( ~ (all_136_0 = all_56_5) | all_56_1 = 0) & ( ~
% 23.72/3.99 | | | | | | | | | (all_56_1 = 0) | all_136_0 = all_56_5)))
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | ALPHA: (115) implies:
% 23.72/3.99 | | | | | | | | | (116) (all_56_3 = empty_set & ~ (all_56_5 = empty_set)) |
% 23.72/3.99 | | | | | | | | | (( ~ (all_136_0 = all_56_5) | all_56_1 = 0) & ( ~
% 23.72/3.99 | | | | | | | | | (all_56_1 = 0) | all_136_0 = all_56_5))
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | BETA: splitting (116) gives:
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | Case 1:
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | (117) all_56_3 = empty_set & ~ (all_56_5 = empty_set)
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | ALPHA: (117) implies:
% 23.72/3.99 | | | | | | | | | | (118) all_56_3 = empty_set
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | REDUCE: (32), (118) imply:
% 23.72/3.99 | | | | | | | | | | (119) subset(all_56_4, empty_set) = 0
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | GROUND_INST: instantiating (10) with all_56_4, simplifying with
% 23.72/3.99 | | | | | | | | | | (25), (119) gives:
% 23.72/3.99 | | | | | | | | | | (120) all_56_4 = empty_set
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | REDUCE: (106), (120) imply:
% 23.72/3.99 | | | | | | | | | | (121) $false
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | CLOSE: (121) is inconsistent.
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | Case 2:
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | (122) ( ~ (all_136_0 = all_56_5) | all_56_1 = 0) & ( ~
% 23.72/3.99 | | | | | | | | | | (all_56_1 = 0) | all_136_0 = all_56_5)
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | ALPHA: (122) implies:
% 23.72/3.99 | | | | | | | | | | (123) ~ (all_136_0 = all_56_5) | all_56_1 = 0
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | BETA: splitting (123) gives:
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | Case 1:
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | (124) ~ (all_136_0 = all_56_5)
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | REDUCE: (112), (124) imply:
% 23.72/3.99 | | | | | | | | | | | (125) $false
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | CLOSE: (125) is inconsistent.
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | Case 2:
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | (126) all_56_1 = 0
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | REDUCE: (65), (126) imply:
% 23.72/3.99 | | | | | | | | | | | (127) $false
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | End of split
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | End of split
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | End of split
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | Case 2:
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | (128) all_56_4 = empty_set & ~ (all_56_5 = empty_set)
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | ALPHA: (128) implies:
% 23.72/3.99 | | | | | | | | (129) all_56_4 = empty_set
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | REDUCE: (106), (129) imply:
% 23.72/3.99 | | | | | | | | (130) $false
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | CLOSE: (130) is inconsistent.
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | End of split
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | End of split
% 23.72/3.99 | | | | | |
% 23.72/3.99 | | | | | Case 2:
% 23.72/3.99 | | | | | |
% 23.72/3.99 | | | | | | (131) all_56_5 = empty_set
% 23.72/3.99 | | | | | |
% 23.72/3.99 | | | | | | BETA: splitting (52) gives:
% 23.72/3.99 | | | | | |
% 23.72/3.99 | | | | | | Case 1:
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | (132) ~ (all_136_1 = 0)
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | REDUCE: (69), (132) imply:
% 23.72/3.99 | | | | | | | (133) $false
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | CLOSE: (133) is inconsistent.
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | Case 2:
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | (134) ( ~ (all_56_3 = empty_set) | all_56_5 = empty_set | (( ~
% 23.72/3.99 | | | | | | | (all_56_1 = 0) | all_56_2 = empty_set) & ( ~
% 23.72/3.99 | | | | | | | (all_56_2 = empty_set) | all_56_1 = 0))) &
% 23.72/3.99 | | | | | | | ((all_56_3 = empty_set & ~ (all_56_5 = empty_set)) | ((
% 23.72/3.99 | | | | | | | ~ (all_136_0 = all_56_5) | all_56_1 = 0) & ( ~
% 23.72/3.99 | | | | | | | (all_56_1 = 0) | all_136_0 = all_56_5)))
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | ALPHA: (134) implies:
% 23.72/3.99 | | | | | | | (135) (all_56_3 = empty_set & ~ (all_56_5 = empty_set)) | (( ~
% 23.72/3.99 | | | | | | | (all_136_0 = all_56_5) | all_56_1 = 0) & ( ~
% 23.72/3.99 | | | | | | | (all_56_1 = 0) | all_136_0 = all_56_5))
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | BETA: splitting (48) gives:
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | | Case 1:
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | (136) all_56_4 = empty_set & ~ (all_56_5 = empty_set)
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | ALPHA: (136) implies:
% 23.72/3.99 | | | | | | | | (137) ~ (all_56_5 = empty_set)
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | REDUCE: (131), (137) imply:
% 23.72/3.99 | | | | | | | | (138) $false
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | CLOSE: (138) is inconsistent.
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | Case 2:
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | (139) ( ~ (all_134_0 = all_56_5) | all_134_1 = 0) & ( ~
% 23.72/3.99 | | | | | | | | (all_134_1 = 0) | all_134_0 = all_56_5)
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | ALPHA: (139) implies:
% 23.72/3.99 | | | | | | | | (140) ~ (all_134_1 = 0) | all_134_0 = all_56_5
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | BETA: splitting (140) gives:
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | | Case 1:
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | (141) ~ (all_134_1 = 0)
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | REDUCE: (67), (141) imply:
% 23.72/3.99 | | | | | | | | | (142) $false
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | CLOSE: (142) is inconsistent.
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | Case 2:
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | (143) all_134_0 = all_56_5
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | COMBINE_EQS: (70), (143) imply:
% 23.72/3.99 | | | | | | | | | (144) all_132_0 = all_56_5
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | SIMP: (144) implies:
% 23.72/3.99 | | | | | | | | | (145) all_132_0 = all_56_5
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | COMBINE_EQS: (131), (145) imply:
% 23.72/3.99 | | | | | | | | | (146) all_132_0 = empty_set
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | COMBINE_EQS: (105), (146) imply:
% 23.72/3.99 | | | | | | | | | (147) all_136_0 = empty_set
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | BETA: splitting (135) gives:
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | | Case 1:
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | (148) all_56_3 = empty_set & ~ (all_56_5 = empty_set)
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | ALPHA: (148) implies:
% 23.72/3.99 | | | | | | | | | | (149) ~ (all_56_5 = empty_set)
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | REDUCE: (131), (149) imply:
% 23.72/3.99 | | | | | | | | | | (150) $false
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | CLOSE: (150) is inconsistent.
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | Case 2:
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | (151) ( ~ (all_136_0 = all_56_5) | all_56_1 = 0) & ( ~
% 23.72/3.99 | | | | | | | | | | (all_56_1 = 0) | all_136_0 = all_56_5)
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | ALPHA: (151) implies:
% 23.72/3.99 | | | | | | | | | | (152) ~ (all_136_0 = all_56_5) | all_56_1 = 0
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | BETA: splitting (152) gives:
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | Case 1:
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | (153) ~ (all_136_0 = all_56_5)
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | REDUCE: (131), (147), (153) imply:
% 23.72/3.99 | | | | | | | | | | | (154) $false
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | Case 2:
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | (155) all_56_1 = 0
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | REDUCE: (65), (155) imply:
% 23.72/3.99 | | | | | | | | | | | (156) $false
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 23.72/3.99 | | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | | End of split
% 23.72/3.99 | | | | | | | | | |
% 23.72/3.99 | | | | | | | | | End of split
% 23.72/3.99 | | | | | | | | |
% 23.72/3.99 | | | | | | | | End of split
% 23.72/3.99 | | | | | | | |
% 23.72/3.99 | | | | | | | End of split
% 23.72/3.99 | | | | | | |
% 23.72/3.99 | | | | | | End of split
% 23.72/3.99 | | | | | |
% 23.72/3.99 | | | | | End of split
% 23.72/3.99 | | | | |
% 23.72/3.99 | | | | End of split
% 23.72/3.99 | | | |
% 23.72/3.99 | | | Case 2:
% 23.72/3.99 | | | |
% 23.72/3.99 | | | | (157) ~ (all_142_2 = 0)
% 23.72/3.99 | | | |
% 23.72/3.99 | | | | REDUCE: (66), (157) imply:
% 23.72/3.99 | | | | (158) $false
% 23.72/3.99 | | | |
% 23.72/3.99 | | | | CLOSE: (158) is inconsistent.
% 23.72/3.99 | | | |
% 23.72/3.99 | | | End of split
% 23.72/3.99 | | |
% 23.72/3.99 | | End of split
% 23.72/3.99 | |
% 23.72/3.99 | End of split
% 23.72/3.99 |
% 23.72/3.99 End of proof
% 23.72/3.99 % SZS output end Proof for theBenchmark
% 23.72/4.00
% 23.72/4.00 3370ms
%------------------------------------------------------------------------------